Estimation of the Duplication History under a Stochastic Model for Tandem Repeats

We present a stochastic model for tandem duplication and substitution mutations that can be used to estimate relative mutation rates and the total number of mutations from a single sequence. Important parameters of the model include the probability of a substitution mutation and the probabilities of tandem duplications of various lengths. Our model indicates that if the probability of substitution mutations is insigni cant, little information can be obtained from a single sequence (which has undergone only tandem duplication). On the other hand, in the presence of both substitution and tandem duplication, one can estimate the parameters of the model, using which we can estimate the total number of mutations of each type. We validate our estimation method via Monte Carlo simulation and show that it outperforms the state of the art algorithm. We also apply our method to the tandem repeat regions in the human genome, where it demonstrates the di erent behavior of microand minisatellites and can be used to compare mutation rates across chromosomes.